Kali builds a tower

[Needgmat]

Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes 1/2 of the green bricks and adds 1/3 more blue bricks, reducing the size of the tower by 14 bricks. How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?

A) 82

B) 96

C) 110

D) 120

E) 192

OAC

Please explain

[GMATGuruNY]

Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes (1/2) of the green bricks and adds (1/3) more blue bricks, reducing the size of the tower by 14 bricks. How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?

A) 82
B) 96
C) 110
D) 120
E) 192

Since the number of green bricks decreases by 1/2, the number of green bricks must be EVEN.
Since the number of blue bricks increases by 1/3, the number of blue bricks must be a MULTIPLE OF 3.
Thus, the MULTIPLIER for the ratio must be an EVEN MULTIPLE OF 3 -- in other words, a MULTIPLE OF 6.

Multiplying R:G:B = 4:3:1 by 6, we get:
R=24, G=18, B=6.
Here, if 1/2 of the green bricks are removed, and the number of blue bricks increases by 1/3, the net change = -(1/2 * 18) + (1/3 * 6) = -9 + 2 = -7.

To double the net change to -14, all of the values in the ratio must also DOUBLE:
R=48, G=36, B=12.
Thus:
T = 48+36+12 = 96 bricks.

After 14 bricks are removed, the remaining number of bricks = 96-14 = 82.
To increase this value to twice the original number of bricks -- 192 -- the number of additional bricks needed = 192-82 = 110.

The correct answer is C.

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Hi Needgmat,

There's a discussion of this question here:

https://www.beatthegmat.com/toy-tower-t270037.html

GMAT assassins aren't born, they're made,
Rich

[Needgmat]

To double the net change to -14, all of the values in the ratio must also DOUBLE:
R=48, G=36, B=12.

Hi GMATGuruNY ,

Can you please advise why do you double the value? Please explain.

Thanks,

Kavin

[DavidG@VeritasPrep]

Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes 1/2 of the green bricks and adds 1/3 more blue bricks, reducing the size of the tower by 14 bricks. How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?

A) 82

B) 96

C) 110

D) 120

E) 192

OAC

Please explain

Algebraically:

Red: 4x
Green: 3x
Blue: x

If we remove half the green, we're removing 3x/2 Green
If we add 1/3 more blue, we're adding x/3 blue.

The net effect here is -14, so (-3x/2) + (x/3) = -14; (-9x + 2x)/6 = -14; -7x = -84; x = 12



So to start we had

Red: 4*12 = 48
Green: 3*12 = 36
Blue: 1*12 = 12
Total = 96

We remove 14 to get 96 - 14 = 82
If we started with 96, double that number would be 192. If we have 82 bricks after removing 14, we need 192 -82 = 110 more. Answer is C

[Matt@VeritasPrep]

To double the net change to -14, all of the values in the ratio must also DOUBLE:
R=48, G=36, B=12.

Hi GMATGuruNY ,

Can you please advise why do you double the value? Please explain.

Thanks,

Kavin

The first change (-1/2 of Green, +1/3 of Blue) nets you -7 blocks total, and you want to double that to -14, so you double the change for each color of block. Mitch is starting with -7 here because he's working with multiples of 6, and the 4:3:1 multiplied by 6 gives a change of -7.